Blender textures are rendered on each triangle individually
When the mesh does not have an UV map, the polygons still have default UV coordinates. The default maps the whole 2D texture to the entire polygon. That's why every face separately repeats what you see in the texture preview.



But to actually get this, coordinate mapping has to be switched to UV.



The procedural wood texture is a 3D texture. It can use 3D coordinates to calculate the color. But only if the coordinate mapping is of a 3D kind. UV is 2D mapping.



The "Object" coordinate mapping is a 3D mapping. Normally it is based on the bounding box of the mesh, but it can be changed in the Texture Space settings for the mesh.